Answer:
[tex]y=\frac{3}{2}x+3[/tex]
Step-by-step explanation:
Take the given equation:
[tex]-3x+2y=6[/tex]
Solve for y so that the equation is written in slope-intercept form:
[tex]y=mx+b[/tex]
m is the slope and b is the y-intercept. x and y are the coordinate points (x,y).
Solve for y:
Add 3x to both sides of the equation:
[tex]-3x+3x+2y=6+3x\\\\2y=3x+6[/tex]
Divide both sides of the equation by 2 to isolate y:
[tex]\frac{2y}{2}=\frac{3x+6}{2} \\\\ y=\frac{3}{2}x+3[/tex]
The slope is [tex]\frac{3}{2}[/tex] and the y-intercept is 3.
To graph, you need two points. You can use the y-intercept as one.
The y-intercept is the place where the line crosses over the y-axis, where x equals 0, so the point is (0,3).
Next, take any value for x and insert it into the equation. We'll use 2:
[tex]y=\frac{3}{2}(2)+3[/tex]
Using this, you can solve for the value of y when x is equal to 2.
Simplify:
[tex]\frac{3}{2} *\frac{2}{1}=\frac{6}{2}=3 \\\\y=3+3\\\\y=6[/tex]
So, when x=2, y is 6 (2,6).
Plot the points (0,3) and (2,6)
Draw a straight line through the two, going past both.
:Done
In the graph, one square is 1 unit
